It's my honor to share some Final Fantasy XIV experience with FFXIV new palyer, I will try my best to help you!

Some General Idea of Progression For A New FFXIV Player

Once you hit 60, you can start collecting Esoteric and Lore tomes. Eso has no weekly cap, Lore has a cap of 450 per week. Esoteric gear is item level 200-210, Lore is 230. Both are obtained by running Lv. 60 dungeons/raids, hunts, and duty roulettes. There used to be Law tomestone items at item level 170-180, but the recent patch uncapping Esoterics made the Esoteric gear far easier to get. Law items are now obtained through Centurio Seals, which are typically far more limited in terms of obtaining them (hunts only).

It's not so much gear progression anymore as it is content progression. Once you hit 60, you can...

- Do hunts (drops tomes, though lore tomes only drop from Heavensward hunts)

- Do the first set of Lv. 60 dungeons: Neverreap and Fractal

- Fight Bismarck and Ravana EX - both drop item level 175-185 weapons, but most parties are after a new mount item from them instead.

- Work on your Anima relic, an item level 200-210 weapon (does not require completion of the Lv. 50 relic, though you can trade one in to skip the first step)

When you hit around item level 170, you can...

- Do Alexander Gordias and the Savage version (first raid tier), though I imagine people hardly do this anymore

At item level 180, you can start doing...

- Void Ark (24-man raid, drops items to upgrade your Esoteric gear to 210 as well as a weekly item to get a grade V materia of your choice)

- Diadem (rather hard to describe, essentially you have an hour to collect as much gear and crafting materials as you can get your hands on, unwanted gear can be exchanged for spoils for other goodies such as grade V materia)

- Second set of Lv. 60 dungeons (Arboretum and Pharos Sirius Hard - latter requires clearing normal mode first, clearing both along with the earlier Lv. 60 dungeons will unlock Lv. 60 Roulette, which is your main source of Esoteric tomes and a secondary source of Lore tomes)

At item level 190, you can start doing...

- EX version of the story trial you do upon hitting Lv. 60 (to mention the name would be spoilers)

- Third set of Lv. 60 dungeons (Anti-tower and Lost City of Amdapor Hard - former requires further progression in the post-60 main quest and latter requires clearing normal mode first, doing both will unlock Expert Roulette, which is your main source of Lore tomes)

At item level 200, you can start doing...

- Sephirot normal and EX trial

- Alexander Midas and the Savage version

For now, take your time, I don't remember if there's anything you can collect now that would allow you to gear up immediately at endgame (besides crafting materials for item level 220 equipment, but those would most likely be way out of your reach).

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16
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I really hope Square Enix does something about the current issue with PvP

Not as frequently no, but releasing it and only updating it once or twice throughout the course of FFXIV Heavensward (as was really the case in FFXIV ARR) will leave it to become a barren wasteland.

At UFFXIV-Talk about the fundamental mess of problems with the new red scrip system

Let's get real, people who were 8/8 50 in Final Fantasy XIV A Realm Reborn were bound to get 8/8 60 fast. They knew this would happen, it is not an error. There is nothing else developed for crafting, they decided to just leave it out.